Wreath products by a Leavitt path algebra and affinizations.
type: Item
instance of: scholarly article
zbMATH Open document ID: 1306.16002
DOI: 10.1142/S0218196714500295
author: Hamed H. Alsulami
author: Adel Alahmadi
published in: International Journal of Algebra and Computation
publication date: 2014-10-15T00:00:00Z
full work available at URL: https://arxiv.org/abs/1404.3869
Mathematics Subject Classification ID: 16D70
Mathematics Subject Classification ID: 16G20
Mathematics Subject Classification ID: 16N40
Mathematics Subject Classification ID: 16S99
Mathematics Subject Classification ID: 46L05
zbMATH DE Number: 6356170
zbMATH Keywords: wreath products of algebras
zbMATH Keywords: Leavitt path algebras
zbMATH Keywords: affine algebras
zbMATH Keywords: non-nil Jacobson radical
zbMATH Keywords: non-nilpotent locally nilpotent radical
MaRDI profile type: Publication
arXiv ID: 1404.3869
cites work: The Leavitt path algebra of a graph.
cites work: Simple Lie algebras arising from Leavitt path algebras.
cites work: Structure of Leavitt path algebras of polynomial growth
cites work: Nonstable \(K\)-theory for graph algebras.
cites work: Examples in finite Gel'fand-Kirillov dimension
cites work: A question of Kaplansky
cites work: Q5569204
OpenAlex ID: W2108163575
title: Wreath products by a Leavitt path algebra and affinizations.
review text: Starting from an associative algebra \(A\) and a graph \(\Gamma=(V,E)\), the authors construct the wreath product \(B:=A\text{\,wr\,}L(\Gamma)\) of \(A\) and the Leavitt path algebra \(L(\Gamma)\). The algebra \(B\) has an ideal \(I\) consisting of (possibly infinite) matrices over \(A\) and such that \(B/I\cong L(\Gamma)\). Moreover if \(W\) is a hereditary subset of the set of vertices of a graph \(\Gamma\), then the Leavitt path algebra \(L(\Gamma)\) can be written as a wreath product of \(L(W)\) with \(L(\Gamma/W)\) (for a suitable notion of quotient graph). The authors take advantage of these facts to construct new examples of (i) affine algebras with non-nil Jacobson radicals, (ii) affine algebras with non-nilpotent locally nilpotent radicals.
reviewed by: Candido Martín González
description: scientific article; zbMATH DE number 6356170